CrossRef Open Access 2024 1 sitasi

Log-concave polynomials III: Mason’s ultra-log-concavity conjecture for independent sets of matroids

Nima Anari Kuikui Liu Shayan Oveis Gharan Cynthia Vinzant

Lihat Sumber DOI

Abstrak

We give a self-contained proof of the strongest version of Mason’s conjecture, namely that for any matroid the sequence of the number of independent sets of given sizes is ultra log-concave. To do this, we introduce a class of polynomials, called completely log-concave polynomials, whose bivariate restrictions have ultra log-concave coefficients. At the heart of our proof we show that for any matroid, the homogenization of the generating polynomial of its independent sets is completely log-concave.

Penulis (4)

Nima Anari

Kuikui Liu

Shayan Oveis Gharan

Cynthia Vinzant

Format Sitasi

APA MLA BibTeX

Anari, N., Liu, K., Gharan, S.O., Vinzant, C. (2024). Log-concave polynomials III: Mason’s ultra-log-concavity conjecture for independent sets of matroids. https://doi.org/10.1090/proc/16724

Akses Cepat

Lihat di Sumber doi.org/10.1090/proc/16724

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Total Sitasi: 1×
Sumber Database: CrossRef
DOI: 10.1090/proc/16724
Akses: Open Access ✓